Effective diffusion coefficients behavior in osmotic dehydration of apple slices considering shrinking and local concentration dependence

The mass transfer during osmotic dehydration of apple slices immersed in 40, 50 and 60% (w/w) aqueous sucrose solutions was investigated to evaluate the influence of solution concentration on diffusivities. In the mathematical model, the diffusion coefficients were functions of the local water and sucrose concentration. The mass transfer equations were, simultaneously, solved for water and sucrose using an implicit numerical method. Material coordinates following the shrinkage of the solid were used. The predicted concentration profiles were integrated and compared to experimental data, showing a reasonable agreement with the measured data. on average, the effective diffusion coefficients for water and sucrose decreased as the osmotic solution concentration increased; that is the behavior of the binary coefficients in water-sucrose solutions. However, the diffusivities expressed as a function of the local concentration in the slices varied between the treatments. Water diffusion coefficients showed a remarkable variation throughout the slice and unusual behavior, which was associated to the cellular structure changes observed in tissue immersed in osmotic solutions. Cell structure changes occurred in different ways: moderate plasmolysis at 40%, accentuated plasmolysis at 50% and generalized damage of the cells at 60%. Intact vacuoles were observed after a long time of exposure (30 h) to 40 and 50% solutions. Effects of the concentration on tissue changes make it difficult to generalize the behavior of diffusion coefficients.

Global dynamics of stationary solutions of the extended Fisher-Kolmogorov equation

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Configuration-dependent diffusion can shift the kinetic transition state and barrier height of protein folding

We show that diffusion can play an important role in protein-folding kinetics. We explicitly calculate the diffusion coefficient of protein folding in a lattice model. We found that diffusion typically is configuration- or reaction coordinate-dependent. The diffusion coefficient is found to be decreasing with respect to the progression of folding toward the native state, which is caused by the collapse to a compact state constraining the configurational space for exploration. The configuration- or position-dependent diffusion coefficient has a significant contribution to the kinetics in addition to the thermodynamic free-energy barrier. It effectively changes (increases in this case) the kinetic barrier height as well as the position of the corresponding transition state and therefore modifies the folding kinetic rates as well as the kinetic routes. The resulting folding time, by considering both kinetic diffusion and the thermodynamic folding free-energy profile, thus is slower than the estimation from the thermodynamic free-energy barrier with constant diffusion but is consistent with the results from kinetic simulations. The configuration- or coordinate-dependent diffusion is especially important with respect to fast folding, when there is a small or no free-energy barrier and kinetics is controlled by diffusion. Including the configurational dependence will challenge the transition state theory of protein folding. The classical transition state theory will have to be modified to be consistent. The more detailed folding mechanistic studies involving phi value analysis based on the classical transition state theory also will have to be modified quantitatively.

Synchronization: Stability and duration time

We consider the problem of stability and duration of the synchronization process between self-excited oscillators, both in their regular and chaotic states. Making use of the properties of Hill equation describing the deviation between the slave and the master, we derive the stability conditions and expressions of the synchronization time. A fairly good agreement is obtained between the analytical and numerical results.

Numerical solution of the two-dimensional Gross-Pitaevskii equation for trapped interacting atoms

We present a numerical scheme for solving the time-independent nonlinear Gross-Pitaevskii equation in two dimensions describing the Bose-Einstein condensate of trapped interacting neutral atoms at zero temperature. The trap potential is taken to be of the harmonic-oscillator type and the interaction both attractive and repulsive. The Gross-Pitaevskii equation is numerically integrated consistent with the correct boundary conditions at the origin and in the asymptotic region. Rapid convergence is obtained in all cases studied. In the attractive case there is a limit Co the maximum number of atoms in the condensate. (C) 2000 Published by Elsevier B.V. B.V. All rights reserved.

Mathematical models of generalized diffusion

We discuss in this paper equations describing processes involving non-linear and higher-order diffusion. We focus on a particular case (u(t) = 2 lambda (2)(uu(x))(x) + lambda (2)u(xxxx)), which is put into analogy with the KdV equation. A balance of nonlinearity and higher-order diffusion enables the existence of self-similar solutions, describing diffusive shocks. These shocks are continuous solutions with a discontinuous higher-order derivative at the shock front. We argue that they play a role analogous to the soliton solutions in the dispersive case. We also discuss several physical instances where such equations are relevant.

Bose-Einstein condensates in 2D with time-periodic scattering length

We discuss two-dimensional Bose-Einstein Condensates (BEC) under time-periodic variation of the scattering length. In particular we argue that for high-frequency variation there exist stable self-confined condensates without an external trap, when the do component of the scattering length is negative. Our results are based on a variational approximation, on direct averaging of the Gross-Pitaevskii equation and on numerical simulations.

Bright solitons in coupled defocusing NLS equation supported by coupling: Application to Bose-Einstein condensation

We demonstrate the formation of bright solitons in coupled self-defocusing nonlinear Schrodinger (NLS) equation supported by attractive coupling. As an application we use a time-dependent dynamical mean-field model to study the formation of stable bright solitons in two-component repulsive Bose-Einstein condensates (BECs) supported by interspecies attraction in a quasi one-dimensional geometry. When all interactions are repulsive, there cannot be bright solitons. However, bright solitons can be formed in two-component repulsive BECs for a sufficiently attractive interspecies interaction, which induces an attractive effective interaction among bosons of same type. (c) 2005 Elsevier B.V. All rights reserved.

Time evolution of the Wigner function in discrete quantum phase space for a soluble quasi-spin model

The discrete phase space approach to quantum mechanics of degrees of freedom without classical counterparts is applied to the many-fermions/quasi-spin Lipkin model. The Wi:ner function is written for some chosen states associated to discrete angle and angular momentum variables, and the rime evolution is numerically calculated using the discrete von Neumnnn-Liouville equation. Direct evidences in the lime evolution of the Wigner function are extracted that identify a tunnelling effect. A connection with a SU(2)-based semiclassical continuous approach to the Lipkin model is also presented.

Bose-Einstein condensation dynamics from the numerical solution of the Gross-Pitaevskii equation

We study certain stationary and time-evolution problems of trapped Bose-Einstein condensates using the numerical solution of the Gross-Pitaevskii (GP) equation with both spherical and axial symmetries. We consider time-evolution problems initiated by suddenly changing the interatomic scattering length or harmonic trapping potential in a stationary condensate. These changes introduce oscillations in the condensate which are studied in detail. We use a time iterative split-step method for the solution of the time-dependent GP equation, where all nonlinear and linear non-derivative terms are treated separately from the time propagation with the kinetic energy terms. Even for an arbitrarily strong nonlinear term this leads to extremely accurate and stable results after millions of time iterations of the original equation.

Free electromagnetic field in Riemannian space-time via DKP theory

We study the massless Duffin-Kemmer-Petiau (DKP) equation in Riemannian space-times, particularly the massless spin 1 sector which reproduces the free Maxwell's equations.

Numerical and variational solutions of the dipolar Gross-Pitaevskii equation in reduced dimensions

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Numerical approximation of the Ginzburg-Landau equation with memory effects in the dynamics of phase transitions

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

BCS-BEC crossover in a trapped Fermi super-fluid using a density-functional equation

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Stochastic quantization of real-time thermal field theory

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)